QuantRS2-Sim: Advanced Quantum Simulation Suite

QuantRS2-Sim is the comprehensive simulation engine of the QuantRS2 quantum computing framework, providing state-of-the-art quantum simulation algorithms, error correction codes, and performance optimization techniques for simulating quantum systems up to 30+ qubits on standard hardware.

Core Features

Multi-Backend Simulation Architecture

• State Vector Simulators: Classical dense state vector simulation with SIMD acceleration
• Matrix Product States (MPS): Memory-efficient simulation for low-entanglement circuits
• Stabilizer Simulators: Exponentially fast simulation for Clifford circuits
• Decision Diagram (DD): Symbolic simulation using quantum decision diagrams
• Tensor Network Simulators: Advanced contraction algorithms for arbitrary network topologies
• Path Integral Methods: Feynman path integral approach for quantum evolution

Advanced Quantum Simulation

• Quantum Monte Carlo: Variational (VMC), diffusion (DMC), and path integral (PIMC) methods
• Trotter-Suzuki Decomposition: Time evolution of quantum systems with optimized decompositions
• Automatic Differentiation VQE: Gradient-based optimization for variational quantum eigensolvers
• Photonic Quantum Computing: Continuous variable and discrete photonic system simulation
• Fermionic Simulation: Second quantization with Jordan-Wigner and Bravyi-Kitaev transformations
• Open Quantum Systems: Lindblad master equation integration for realistic quantum dynamics

Error Correction & Fault Tolerance

• Quantum Error Correction: Surface, color, and concatenated codes
• Noise Models: Comprehensive realistic noise modeling including correlated errors
• Error Mitigation: Zero-noise extrapolation, virtual distillation, and symmetry verification
• Process Tomography: Quantum channel characterization and benchmarking
• Quantum Volume: IBM's quantum volume protocol

Performance & Verification

• Quantum Supremacy: Cross-entropy benchmarking and Porter-Thomas verification
• Hardware Optimization: SIMD acceleration, memory-efficient algorithms, and GPU computing
• SciRS2 Integration: Advanced linear algebra operations using optimized BLAS/LAPACK
• Quantum Debugging: Interactive debugging tools with breakpoints and state inspection
• Performance Profiling: Comprehensive benchmarking and optimization analysis

Usage Examples

Basic State Vector Simulation

use quantrs2_sim::prelude::*;

fn basic_simulation() -> Result<()> {
    // Create a Bell state circuit
    let mut simulator = StateVectorSimulator::new();
    
    // Apply gates directly
    simulator.h(0)?;
    simulator.cnot(0, 1)?;
    
    // Measure and get probabilities
    let probabilities = simulator.probabilities();
    for (state, prob) in probabilities.iter().enumerate() {
        println!("|{:02b}⟩: {:.6}", state, prob);
    }
    
    Ok(())
}

Matrix Product State (MPS) Simulation

use quantrs2_sim::prelude::*;

fn mps_simulation() -> Result<()> {
    // MPS is memory-efficient for low-entanglement circuits
    let config = MPSConfig {
        max_bond_dimension: 64,
        compression_threshold: 1e-12,
    };
    
    let mut simulator = EnhancedMPSSimulator::new(10, config);
    
    // Create a low-entanglement circuit
    for i in 0..10 {
        simulator.h(i)?;
        if i > 0 {
            simulator.cnot(i-1, i)?;
        }
    }
    
    let result = simulator.measure_all(1000)?;
    println!("MPS simulation completed with bond dimension: {}", 
             simulator.max_bond_dimension());
    
    Ok(())
}

Stabilizer Simulation for Clifford Circuits

use quantrs2_sim::prelude::*;

fn stabilizer_simulation() -> Result<()> {
    // Exponentially fast simulation for Clifford circuits
    let mut simulator = StabilizerSimulator::new(10);
    
    // Apply Clifford gates
    simulator.h(0)?;
    simulator.cnot(0, 1)?;
    simulator.s(1)?;
    
    // Check if circuit is still Clifford
    if simulator.is_clifford() {
        let measurements = simulator.measure_all(1000)?;
        println!("Clifford simulation: {} measurements", measurements.len());
    }
    
    Ok(())
}

Quantum Monte Carlo Simulation

use quantrs2_sim::prelude::*;

fn quantum_monte_carlo() -> Result<()> {
    // Variational Monte Carlo for ground state estimation
    let hamiltonian = HamiltonianLibrary::heisenberg_chain(8, 1.0, 1.0, 1.0);
    let wave_function = WaveFunction::jastrow_gutzwiller(8);
    
    let mut vmc = VMC::new(hamiltonian, wave_function);
    let result = vmc.run(10000)?;
    
    println!("Ground state energy: {:.6} ± {:.6}", 
             result.energy, result.energy_error);
    
    Ok(())
}

Automatic Differentiation VQE

use quantrs2_sim::prelude::*;

fn autodiff_vqe() -> Result<()> {
    // VQE with automatic gradient computation
    let hamiltonian = HamiltonianLibrary::hydrogen_molecule(1.4);
    let ansatz = ansatze::hardware_efficient_ansatz(4, 2);
    
    let mut vqe = VQEWithAutodiff::new(hamiltonian, ansatz);
    vqe.set_gradient_method(GradientMethod::ParameterShift);
    
    let result = vqe.optimize(100)?;
    println!("VQE converged to energy: {:.6} in {} iterations", 
             result.final_energy, result.iterations.len());
    
    Ok(())
}

Noise Simulation and Error Mitigation

use quantrs2_sim::prelude::*;

fn noise_and_mitigation() -> Result<()> {
    // Create realistic noise model
    let noise_model = RealisticNoiseModelBuilder::new()
        .add_depolarizing_error(0.001)
        .add_thermal_relaxation(50e-6, 70e-6, 20e-9)
        .add_readout_error(0.02, 0.03)
        .build();
    
    let mut simulator = StateVectorSimulator::new_with_noise(noise_model);
    
    // Run circuit multiple times for statistics
    let mut results = Vec::new();
    for _ in 0..1000 {
        simulator.reset();
        simulator.h(0)?;
        simulator.cnot(0, 1)?;
        results.push(simulator.measure_all(1)?);
    }
    
    // Apply zero-noise extrapolation
    let extrapolator = ZeroNoiseExtrapolator::new();
    let mitigated_result = extrapolator.extrapolate(&results)?;
    
    println!("Mitigated expectation value: {:.6} ± {:.6}",
             mitigated_result.value, mitigated_result.error);
    
    Ok(())
}

Quantum Supremacy Verification

use quantrs2_sim::prelude::*;

fn quantum_supremacy_verification() -> Result<()> {
    // Generate random quantum circuit for supremacy testing
    let params = VerificationParams {
        width: 20,
        depth: 20,
        gate_set: GateSet::GoogleSycamore,
    };
    
    let verifier = QuantumSupremacyVerifier::new(params);
    let circuit = verifier.generate_random_circuit()?;
    
    // Verify using cross-entropy benchmarking
    let ce_result = verifier.cross_entropy_benchmark(&circuit, 1000000)?;
    
    if ce_result.is_quantum_advantage() {
        println!("Quantum advantage detected! XEB = {:.6}", ce_result.xeb_value);
    }
    
    Ok(())
}

Photonic Quantum Computing

use quantrs2_sim::prelude::*;

fn photonic_simulation() -> Result<()> {
    // Continuous variable photonic simulation
    let config = PhotonicConfig {
        cutoff_dimension: 10,
        method: PhotonicMethod::FockBasis,
    };
    
    let mut simulator = PhotonicSimulator::new(4, config);
    
    // Apply photonic operations
    simulator.displacement(0, Complex64::new(1.0, 0.5))?;
    simulator.squeezing(1, 0.5)?;
    simulator.beam_splitter(0, 1, 0.5)?;
    
    let result = simulator.measure_photon_number_distribution()?;
    println!("Photonic simulation completed with {} modes", result.modes);
    
    Ok(())
}

Comprehensive Module Structure

Core Simulation Engines

• statevector.rs: Dense state vector simulation with SIMD optimizations
• enhanced_statevector.rs: Enhanced state vector with lazy evaluation and memory optimization
• mps_simulator.rs: Basic matrix product state simulator
• mps_basic.rs: Lightweight MPS simulator for low-entanglement circuits
• mps_enhanced.rs: Advanced MPS with optimized contraction algorithms
• stabilizer.rs: Stabilizer formalism for exponentially fast Clifford simulation
• clifford_sparse.rs: Sparse representation of Clifford operations
• decision_diagram.rs: Quantum decision diagram symbolic simulation

Advanced Simulation Methods

• qmc.rs: Quantum Monte Carlo methods (VMC, DMC, PIMC)
• path_integral.rs: Feynman path integral simulation techniques
• trotter.rs: Trotter-Suzuki decomposition for time evolution
• photonic.rs: Photonic quantum computing simulation (continuous variables)
• fermionic_simulation.rs: Second quantization with Jordan-Wigner transforms
• open_quantum_systems.rs: Lindblad master equation integration

Error Correction & Noise

• error_correction/: Comprehensive quantum error correction codes
  • codes.rs: Surface, color, and concatenated codes
  • mod.rs: Error correction framework and utilities
• noise.rs: Basic noise models (bit-flip, phase-flip, depolarizing)
• noise_advanced.rs: Realistic device noise models with correlations
• noise_extrapolation.rs: Zero-noise extrapolation and error mitigation

Optimization & Performance

• optimized_simd.rs: SIMD-accelerated quantum operations
• optimized_chunked.rs: Memory-efficient chunked processing
• optimized_simple.rs: Simplified optimized simulators
• specialized_gates.rs: Hardware-optimized gates
• specialized_simulator.rs: Simulator with specialized gate optimizations
• fusion.rs: Gate fusion optimization for reduced circuit depth
• precision.rs: Adaptive precision control for state vectors

Variational & Machine Learning

• autodiff_vqe.rs: Automatic differentiation for variational quantum eigensolvers
• pauli.rs: Pauli string operations and expectation value computation

Hardware Integration

• gpu.rs: GPU-accelerated simulation using WGPU compute shaders
• gpu_linalg.rs: GPU linear algebra operations for quantum simulation
• scirs2_integration.rs: SciRS2 backend integration for high-performance computing
• scirs2_qft.rs: SciRS2-accelerated quantum Fourier transform
• scirs2_sparse.rs: Sparse matrix operations using SciRS2
• scirs2_eigensolvers.rs: Spectral analysis and eigenvalue computations

Verification & Benchmarking

• quantum_supremacy.rs: Cross-entropy benchmarking and Porter-Thomas verification
• quantum_volume.rs: IBM quantum volume protocol
• benchmark.rs: Performance benchmarking across different simulation methods
• debugger.rs: Interactive quantum debugging with breakpoints and state inspection

Utility & Analysis

• shot_sampling.rs: Statistical sampling and measurement simulation
• sparse.rs: Sparse matrix representations for large quantum systems
• linalg_ops.rs: Linear algebra operations optimized for quantum simulation
• utils.rs: Common utilities and helper functions
• tensor.rs: Tensor manipulation utilities
• tensor_network/: Advanced tensor network contraction algorithms
  • contraction.rs: Optimal contraction order algorithms
  • opt_contraction.rs: Optimized contraction algorithms
  • tensor.rs: Tensor data structures and operations
• dynamic.rs: Dynamic qubit allocation and circuit optimization

Feature Flags

• default: Optimized simulators with SIMD acceleration
• gpu: GPU acceleration using WGPU compute shaders (CUDA/OpenCL/Vulkan)
• simd: Platform-specific SIMD instructions for vectorized operations
• optimize: Advanced optimization algorithms and memory management
• memory_efficient: Large state vector optimizations for 25+ qubit simulation
• advanced_math: SciRS2 integration with optimized BLAS/LAPACK operations
• mps: Matrix Product State simulation with linear algebra support

Performance Characteristics

Simulation Capabilities

• State Vector: Up to 30+ qubits on standard hardware (16GB RAM)
• MPS: 50+ qubits for low-entanglement circuits with bond dimension control
• Stabilizer: Unlimited qubits for Clifford circuits (exponential speedup)
• Decision Diagram: Symbolic simulation with compact representations
• GPU Acceleration: 10-100x speedups for 20+ qubit circuits on compatible hardware

Optimization Features

• SIMD Vectorization: AVX2/AVX-512 support for parallel complex arithmetic
• Multi-threading: Rayon-based parallelization across CPU cores
• Memory Efficiency: Chunked processing and lazy evaluation for large circuits
• Gate Specialization: Hardware-optimized processing for common gates
• SciRS2 Integration: Professional-grade linear algebra with Intel MKL/OpenBLAS

Benchmarking Results

• Single-qubit gates: ~10ns per operation (SIMD optimized)
• Two-qubit gates: ~50ns per operation (depending on entanglement)
• GPU acceleration: 20-50x speedup for 25+ qubit state vector simulation
• MPS simulation: 100x memory reduction for product states

Advanced Simulation Features

Quantum Algorithm Support

• VQE: Automatic differentiation with gradient-based optimization
• QAOA: Optimized Hamiltonian evolution with Trotter decomposition
• Quantum Monte Carlo: Ground state estimation with statistical analysis
• Quantum Supremacy: Cross-entropy benchmarking with statistical verification

Error Correction & Mitigation

• Surface Codes: Topological error correction with syndrome decoding
• Zero-Noise Extrapolation: Richardson extrapolation for error mitigation
• Virtual Distillation: Quantum error mitigation using symmetry verification
• Process Tomography: Complete characterization of quantum channels

Hardware-Aware Simulation

• Device Noise Models: Realistic simulation matching hardware specifications
• Calibration Integration: Real-time hardware parameter updates
• Cross-Platform GPU: WGPU backend supporting CUDA, OpenCL, and Vulkan
• Memory Hierarchy: Cache-aware algorithms for optimal performance

Integration with QuantRS2 Ecosystem

Core Module Integration

• Leverages advanced gate decomposition algorithms for simulation optimization
• Uses optimized matrix representations from core for maximum performance
• Integrates quantum error correction codes for fault-tolerant simulation

Circuit Module Integration

• Simulates circuits with automatic optimization pass selection
• Supports circuit compilation with hardware-aware gate translation
• Provides feedback for circuit optimization based on simulation performance

Device Module Integration

• Accurately simulates real quantum hardware with calibrated noise models
• Provides device characterization through quantum volume and benchmarking
• Supports cloud quantum computer simulation with realistic latency models

Machine Learning Module Integration

• Optimized simulation for variational quantum algorithms
• Automatic differentiation support for quantum neural network training
• Quantum kernel methods with efficient expectation value computation

Research & Development Applications

Quantum Computing Research

• Novel algorithm development with comprehensive simulation backends
• Quantum advantage verification with statistical confidence intervals
• Error correction threshold estimation with realistic noise models

Quantum Chemistry & Physics

• Molecular simulation using fermionic operators and transformations
• Condensed matter physics with many-body quantum systems
• Quantum field theory simulation using path integral methods

Quantum Machine Learning

• Quantum neural network training with automatic differentiation
• Quantum kernel methods for classical machine learning
• Variational quantum algorithm optimization and benchmarking

License

This project is licensed under either:

• Apache License, Version 2.0
• MIT License

at your option.